## airyana1114 one year ago Can someone help me solve this equation? Step by Step.

1. misty1212

HI!!

2. misty1212

is it a hard equation ?

3. airyana1114

$\sqrt{x+6}-4=x$

4. misty1212

oh no that can't be that hard

5. airyana1114

Can you help me? I've never had this type of equation equaled to x and it sort of makes me nervous. Can you walk me through it? @misty1212

6. misty1212

yeah no problem first step is to get the radical by itself on one side of the equation by adding 4 to both sides, i.e. write $\sqrt{x+6}=x+4$

7. misty1212

now you want to do it the math teacher way , or you want to think what the answer is , or both?

8. airyana1114

I'm not sure I understand what you're asking.

9. misty1212

we can find the answer in our head, but that is probably not what your math teacher wants you to do ,so lets go ahead and solve it the way they do in math class

10. airyana1114

Okay

11. misty1212

12. airyana1114

Alright thanks :)

13. misty1212

you want to get rid of the radical, so square both sides (carefully)

14. airyana1114

How would I square (x+4). Like this? x^2+8

15. misty1212

$\sqrt{x+6}=x+4$ square and get $x+6=(x+4)^2$ or $x+6=(x+4)(x+4)$ or $x+6=x^2+8x+16$

16. airyana1114

Where did the 8x come from?

17. misty1212

no dear that is not how you square $$x+4$$ you have to write it as $x(x+4)(x+4)=x^2+4x+4x+16=x^2+8x+16$

18. misty1212

it is that old "first outer inner last" stuff

19. airyana1114

Ohhhh, FOIL okay..that makes sense.

20. misty1212

so now we have $x+6=x^2+8x+16$ which is a quadratic equation we have to solve

21. misty1212

set it equal to zero, get $x^2+7x+10=0$ then factor

22. misty1212

$x^2+7x+10=0\\ (x+2)(x+5)=0$ so $x=-2,x=-5$ but we are not done yet

23. misty1212

you have to check the answer in the original equation not the quadratic equation if you do, you will see that $$x=-2$$ works but $$x=-5$$ does not

24. airyana1114

Making it an extraneous solution correct?

25. misty1212

right , which is a silly way of saying it is not a solution but no matter

26. airyana1114

:) thank you @misty1212

27. misty1212

$\color\magenta\heartsuit$